Must have been a Jayco salesman. I am not aware of a four-season line from that manufacturer, and certainly not everything they make is designed for winter use.
The majority of trailers now are covered underneath, since "enclosed underbody" became a buyer checkpoint. Covering might be a plastic sheet, or maybe non-woven fabric. Enclosed space might be less than 2 inches deep, not heated, but it can be said to be enclosed.
For winter use, I would prefer a four season design, e.g. dual pane windows, fewer and smaller windows and vents, thicker walls with better insulation, plumbing installed in heated spaces, etc. Not all four season RVs ate the same, some are much better at dealing with cold weather than others.
Yes, they are hard to find, few manufacturers build for this market, few buyers want to pay the extra cost, carry the extra weight, and live in the less bright and airy box.
Two manufacturers come to mind, Bigfoot and Northwood. For TTs, and Northwood makes some fivers. Prices might be 50% to 100% higher than low cost, high volume model for similar sizes. If you need something bigger than what these manufactuers provide, there are premium builders who build custom RVs for full-time year-round use. Expect to at least double the cost again.
It also comes down to winter where? Many RVs are used as winter residences, taken to places with warm or at least mild winters.